The theoretical developments in this paper build on two strands of literature.
Our results for consistent estimation and for
constructing confidence sets are based on recent developments in estimation
and inference for general set-identified parameters in the partial
identification literature in econometrics; our approach relies in
particular on the pioneering work of [1]}
and [2]} (for further related references, see the
recent survey of this literature in [3]}).
The research in the partial identification literature does not, however,
consider minimax problems such as (REF ) or GANs.
General minimax problems (but no GANs)
have previously been considered in the stochastic programming literature in operations
research. Our results are particularly closely related to those
in [4]} and [5]}
who consider consistent estimation (but no confidence sets) in minimax
problems, as well as to the foundational results for minimization problems
in [6]}. Further comparison to all these
previous works will be given later in the paper.
